The Incompressible Navier–Stokes Equations on Non-compact Manifolds

By Vittoria Pierfelice. Journal of Geometric Analysis, 2014

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We shall prove dispersive and smoothing estimates for vectorial heat equations associated with Bochner type Laplacians on some non-compact Riemannian manifolds with negative Ricci curvature, in particular on hyperbolic spaces. The negative curvature yields better large time decay than in the Euclidean case. Besides their own known interest in harmonic analysis, these estimates will be used to prove Fujita–Kato type theorems for the incompressible Navier–Stokes equations. We shall also discuss the uniqueness of Leray weak solutions in the two-dimensional case.

Subfields: Applied Mathematics, Mathematical Physics

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